Question

A bicycle and rider have a combined potential energy of 1400 J. What is the potential energy if the bicycle and rider have one fourth their mass at the same height?

Answer 1

The potential energy of 1400 J can be expressed as

$$E=mgh,$$

the energy of reduced mass is

$$E_r=\frac m4gh.\\\space\\ \frac E{E_r}=4,\\\space\\ E_r=\frac E4=350\text{ J}.$$